Mathematics 1201
Unit 1 Lesson 7
Volume
Sphere and Hemisphere
Volume of a Sphere:
The Beetle Sphere: An Actual 1953 VW Beetle Formed into a Perfect Sphere by Ichwan Noor.
The volume, V , of a sphere with radius r is
V 
Example 1:
4 3
r
3
The moon approximates a sphere with diameter 2160 mi. What is the
approximate volume of the moon?
Step 1:
Write formula.
4
V  r 3
3
Step 2:
Find any missing information.
Divide the diameter by two to find the radius.
d  2160
r
d 2160

 1080
2
2
Step 3:
Fill out formula and use your calculator to find the volume.
4
3
V   1080
3
4
V   1,259,712,000
3
V  5,276,669,286.45
exponents 1st,  the top and  by 3.
V  5.28  10 9
The approximate volume is 5.28  10 9 mi3.
Volume of a Hemisphere
Volume of a hemisphere is half the volume of a sphere.
14 3
 r
23
2
 r 3
3
Determining the Surface Area and Volume of a Hemisphere.
Volume of a hemisphere 
Example 2:
A hemisphere has a radius 5.0 cm.
A)
What is the surface area of the hemisphere to the nearest tenth of a
square centimeter?
B)
What is the volume of the hemisphere to the nearest tenth of a
cubic centimetre?
A)
Step 1:
Write formula.
S . A.  3r 2
Step 2:
Fill out formula and solve.
2
S . A.  3 5
S . A.  3 25
S . A.  75
S . A.  235.62
The surface area of the hemisphere is 235.6 cm2.
B)
Step 1:
Write formula
2
V  r 3
3
Step 2:
Fill out formula and solve.
2
3
V   5
3
2
V   125
3
1
V  83 
3
V  261.80
The volume of the hemisphere is 261.8 cm2
Example 3:
What is the diameter of Earth at the equator if the volume of the
hemisphere is 546,720,131,966.58 km2?
Step 1:
Write and fill out formula to solve for the radius.
S . A.  3r 2
384,953,934.26  3r 2
384,953,934.26 3r 2

3
3
40,844,881  1r 2
isolate r ,  by 3 then take
40,844,881  r 2
6,391  r
Step 2:
Find the diameter using the radius from the step one.
diameter is twice the radius
d  2r
d  26,391
d  12,782
The diameter of the Earth at the equator is 12,782 km.
Seatwork/Homework: P. 51-52 #3-20 even